The present invention relates to protective control method and apparatus, in which AC voltage or current of an electric power system is periodically sampled and stored, and the stored sample value is used in combination with the sample value at a time point a predetermined time interval after the stored sampled value for arithmetic operation.
Conventional systems for periodically sampling AC voltages and currents of a commercial frequency of an electric power system and performing arithmetic operation on the sampled values for the purpose of protection of the power system include digital-type protective relays to protect the power system from short-circuiting or grounding fault, digital-type fault-point locating systems to determine the distance to the fault point, and fault data outputting systems for outputting a function showing the phase-relationship of the voltages and currents during the fault relative to the voltages before the fault.
The sampling frequency is generally set to be an integral multiple of the rated commercial frequency, and is not varied even when the operating frequency varies. Sample values are generally stored and used for arithmetic operation. In some of the systems, each of the stored sample value is used, as a predicted value, in combination with another sample value sampled m/2 (m being a positive integer) times the rated period after the stored sample value.
Examples of systems which use such a combination of a stored sample value (as a predicted value) and the subsequent sample value are given below:
(1) Variation over-current relay
This relay operates when the variation in the vector of an AC current exceeds a predetermined value, i.e., when EQU .vertline.I.sub..DELTA. .vertline.=.vertline.I-I'.vertline. &gt;K.sub.1( 1)
Here,
I.sub.66 represents the vector value of a change of the current; PA1 I represents the vector value of the current after the change; PA1 I' represents the vector value of the current before the change; and PA1 K.sub.1 represents a positive constant. PA1 .vertline.I.sub.A .vertline. represents an absolute value of the vector I.sub.66. PA1 n represents natural number; PA1 Y.sub.m represents the predicted value for a specific time point; PA1 S.sub.o represents a sample value in advance of the specific time point by m/2 times the period of the rated frequency; PA1 S.sub.l represents a value equal to (-1).sup.l times the sample value at a time point in advance of the specific time point by l+m/2 times the period of the rated frequency; and PA1 K.sub.o and K.sub.l represent constants satisfying the following relationship: ##EQU11## where .epsilon. represents the permissible range of error for the predicted value which may occur when the power system is operating at the rated frequency.
(2) Close-point fault direction discriminating system
The system determines the product of a stored sample value of a voltage V' before a fault and a sample value of a current I after the fault to disminate the direction of the fault. In place of the current, a difference between a stored sample value of the current I' before the fault and a sample value of the current I after the fault, i.e., an instantaneous value of a current variation I.sub..DELTA. may be used. In this connection, reference is made to Japanese Patent Application Laid-open No. 123418/1984 (Application No. 230022/1982).
(3) Fault-point locating system
The system determines a current variation I.sub.66 which is the difference between a pre-fault current I' and a post-current I and uses it in combination with a post-fault voltage V and current I to determine the distance to the fault point. Reference is made to Japanese Patent Application Publication No. 29471/1983 (Application No. 132575/1978).
(4) Fault data outputting system
The system outputs a function, such as VIcos.theta., V'Isin.theta. or Icos.theta., which shows the relationship of the phase angle .theta. of the voltage V and the current I during a fault relative to a pre-fault voltage V'.
How the stored sample values of a current and a voltage before the variation are obtained is now described with reference to the drawings.
FIG. 9 shows sampling time points against an AC electric quantity. Here it is assumed that 12 samples are taken during one rated period of the commercial frequency. (12 samples/period is assumed in the rest of the specification unless otherwise specified). In FIG. 8, e' and e respectively represent an electric quantity (voltage or current) before and after a change due for example to a fault. (n-2)12, (n-1)1, . . . (n-1)12, (n)1, . . . (n)12, (n+1)1 represent sampling time points. The value of the latter part 1, 2, . . . 11, 12 is increased by 1 or is changed from 12 to 1 every one sampling period and indicates the order of sampling within each period of the rated frequency. The value of the former part, e.g., (n-2), (n-1), (n), (n+1), . . . , is increased by 1 each time the value of the latter part is changed from 12 to 1. For instance, the sampling time points (n-1)1 and (n)1 are apart from each other by one rated period. The sampling time points (n)1 and (n)2 are apart from each other by one sampling interval or 1/12 times one rated period. The stored sample value used as a predicted value for a sampling time point, say (n)6, is one of sample values at sampling time points m/2 times the rated period before (n)6, i.e., (n-1)12, (n-1)6, (n-2)12, . . . Where m is an even number, the sample value is used without change. Where m is an odd number, the sample value is used with its sign (+ or -) inverted. These stored sample values or predicted values equal the sample value at (n)6 if there occurs no change in the electric quantity e'.
Examples of equations for determining variation sample values are given below: EQU e".sub.(n)6 =e.sub.(n)6 +e'.sub.(n-1)12 ( 2) EQU e".sub.(n)6 =e.sub.(n)6 -3'.sub.(n-1)6 ( 3) EQU e".sub.(n)6 =e.sub.(n)6 +e'.sub.(n-2)12 ( 4)
Here, e".sub.(n)6 is a variation sample value at (n)6. e(n)6 is a sample value of the quantity e at (n)6. e'.sub.(n-1)12, e'.sub.(n-1)6 and e'.sub.(n-2)12 are sample values of the quantity e' at (n-1)12, (n-1)6 and (n-2)12. The variation sample value e".sub.(n)6 equals an instantaneous value (which is also called in this specification "a sample value") of a variation quantity EQU e"=e-e' (5)
at (n)6. Usually, a plurality of sample values are used for arithmetic operation, so that a plurality of predicted values are used.
Each of the stored sample values or predicted values for a certain time point, say (n)6, equals a sample value of the same time point (n)6 if the operating frequency is maintained at the rated frequency. If, however, the operating frequency deviates from the rated frequency, there occurs an error since the sampling frequency is fixed.
FIG. 10 shows how an error occurs when the operating frequency differs from the rated frequency. The same reference characters as in FIG. 9 have similar significances, but the sampling time points (n)1 through (n)12 and (n-1)1 through (n-1)12 are plotted within the same period of the same waveform of e' for easier understanding of the error. It is assumed that no change occurs in e'.
Assume that the sampling time point (n)1 is .theta..sub.1 (electrical angle) after the crossing of e' through zero line from negative to positive. The respective sample values will then be as follows: ##EQU3## Here, E' is the peak value of e', .theta..sub.s is the sampling interval in terms of electrical angle of the operating frequency of the power system.
If the operating frequency is f, and the rated frequency is f.sub.o, then ##EQU4## Here, h=1, 2, . . . 12.
The sample values e'.sub.(n-1)1, e'.sub.(n-1)2, e'.sub.(n-1)3 will therefore equal the samples of e' taken in advance of the sample values e.sub.(n)1', e.sub.(n)2 ', e.sub.(n)3 ' by ##EQU5##
In other words, the sample values e' taken one rated period before a specific time point equal the sample values of an imaginary value leading e' by ##EQU6## at the specific time point.
Similarly, the sample values of time points (m/2.times.one rated period) before the specific time point are given by the following equation: ##EQU7##
e'.angle..sup.m.theta. e represents an (imaginary) quantity leading e' by an angle m.theta..sub.e, and is also expressed by e'.epsilon..sup.jm.theta. e.
If, therefore, the sample value taken at a time point (m/2.times.one rated period) before the specific time point and multiplied by (-1).sup.m is used as the predicted value for the specific time point, a phase error of m.theta..sub.e occurs and the error of the predicted value from the sample value is a sample value (an instantaneous value) at the specific time point of a stored error e'.sub.e given by the following equation: ##EQU8## The magnitude .vertline.e'.sub.e .vertline. of e' is therefore given by: ##EQU9## Thus, the ratio of .vertline.e'.sub.e .vertline. to .vertline.e'.vertline. is .vertline.2sin/m2.theta..sub.e .vertline..
Many of the digital relays use a plurality of samples in an arithmetic operation. Besides, a filter is used to prevent an error due to harmonics. Moreover, the electric quantities are in transient state for about 1/2 cycle (period) when there occurs a change in e'. As a result, variation sample values determined in accordance with Eq. (2), (3) or (4) using the sample values during transition will not properly reflect the variation quantity e". For this reason, m is often set to satisfy m.gtoreq.2.
Moreover, it is generally required that characteristics of protective relays be guaranteed even when the operating frequency deviates by -2% or .+-.5%. If m=2 and the frequency deviation is 5%, then m.theta..sub.e =18.degree. and the error .vertline.e'.sub.e .vertline. is as large as 31%. If m=2 and the frequency deviation is 2%, then m.theta..sub.e =7.2.degree. and the error is 12.8%.